Cyclic stress–strain relationship of 63Sn37Pb solder under biaxial proportional and non-proportional loading

Uniaxial, torsional and multiaxial non-proportional loading tests are carried out at room temperature. With the comparison of the load and torque response between proportional and three non-proportional loading conditions, it can be concluded that the materials exhibit non-additional cyclic hardening effect under non-proportional loading compared with proportional loading. A 3-D finite element model of tin–lead solid specimen is established to verify the validity of shear stress approximation on the surface of solid specimen under proportional and non-proportional loading, and a completely strain control is accomplished in finite element model by using soft sensors. The accurate correlation of load–strain and torque–strain curve to experiment indicates that an isotropic and non-linear kinematic hardening model, Chaboche model, can be implemented to describe plastic deformation. The maximum error of shear stress calculation between mathematic approximation and the stress obtained from finite element analysis under various loading conditions is within 7%, which proves that the approximate expression for shear stress is feasible under both proportional and non-proportional loading.